A paper by one of the inventors, E. Betzig, Opt. Lett. 20, 237 (1995), which is incorporated herein by reference for all purposes, described a method to improve the m-dimensional spatial resolution in the image of a sample that includes a dense set of discrete emitters (e.g., fluorescent molecules) by first isolating each discrete emitter in an (m+n)-dimensional space defined by the m spatial dimensions and n additional independent optical properties (e.g., excitation or emission polarization or wavelength of the illumination light, fluorescence lifetime of the fluorescent molecules, etc.). After isolation, the m spatial coordinates of each emitter can be determined with an accuracy dependent upon the signal-to-noise-ratio (SNR) of the imaging apparatus, but generally much better than the original spatial resolution defined by the m-dimensional diffraction limited resolution volume (“DLRV”) of the imaging optics. The map of all spatial coordinates determined in this manner for all emitters then yields a superresolution image of the sample in the m-dimensional position space.
Successful isolation of each emitter by this approach requires a mean volume per emitter in m+n space that is larger than the (m+n)-dimensional point spread function PSF. Consequently, a high molecular density of emitters (e.g. fluorescent molecules) in the sample requires high (m+n)-dimensional resolution by the imaging optics. In the 1995 paper by Betzig, it was estimated that emitting molecules having molecular density of about 1 molecule per cubic nanometer nm could be isolated with near-field microscopy/spectroscopy at cryogenic temperatures (e.g., 77 K) if the molecules were located in a matrix that introduced sufficient inhomogeneous spectral broadening. However, with conventional optical microscopy and the broad molecular spectra that exist under ambient conditions, the density of most target molecular species would be far too high for this approach to be used.